Axial stress & strain worksheet with answers

Free printable Axial stress & strain worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
100 kNØ20120 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
Ø 16 mm0.5 mP = 25 kN

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 25 kNd = 16 mm
σ = MPa
3.Medium
Ø 10 mmSteel2.5 mP = 35 kN

Find the axial strain ε in the steel bar, in microstrain (µε = 10⁻⁶).

P = 35 kNd = 10 mmL = 2.5 mE = 200 GPa
ε = µε
4.Medium
300 kNØ30120 GPaØ80/60400 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
P = ?Ø2070 GPaØ120/50800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø50 mm, E = 70 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
Ø 30 mmAluminium2 mØ 16 mmBrass1 mP = 115 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 115 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 46.47 MPa
  2. 2. σ = 124.3 MPa
  3. 3. ε = 2228 µε
  4. 4. δ = 0.2961 mm
  5. 5. Pmax = 717.1 kN
  6. 6. δ = 10.37 mm

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